Question: Solve for $x$ and $y$ using elimination. $\begin{align*}2x+6y &= -4 \\ 3x-6y &= 6\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $5x = 2$ Divide both sides by $5$ and reduce as necessary. $x = \dfrac{2}{5}$ Substitute $\dfrac{2}{5}$ for $x$ in the top equation. $2( \dfrac{2}{5})+6y = -4$ $\dfrac{4}{5}+6y = -4$ $6y = -\dfrac{24}{5}$ $y = -\dfrac{4}{5}$ The solution is $\enspace x = \dfrac{2}{5}, \enspace y = -\dfrac{4}{5}$.